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Convex Analysis: Theory and Applications

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G. G. Magaril-Il’yaev; V. M. Tikhomirov

This book is an introduction to convex analysis and some of its
applications. It starts with basic theory, which is explained within the
framework of finite-dimensional spaces. The only prerequisites are basic
analysis and simple geometry. The second chapter presents some applications of
convex analysis, including problems of linear programming, geometry, and
approximation. Special attention is paid to applications of convex analysis to
Kolmogorov-type inequalities for derivatives of functions in one
variable. Chapter 3 collects some results on geometry and convex analysis in
infinite-dimensional spaces. A comprehensive introduction written “for
beginners” illustrates the fundamentals of convex analysis in
finite-dimensional spaces.

The book can be used for an advanced undergraduate or graduate-level course
on convex analysis and its applications. It is also suitable for independent
study of this important area of mathematics.

Readership

Advanced undergraduates, graduate students and research
mathematicians interested in convex analysis.

This book is an introduction to convex analysis and some of its
applications. It starts with basic theory, which is explained within the
framework of finite-dimensional spaces. The only prerequisites are basic
analysis and simple geometry. The second chapter presents some applications of
convex analysis, including problems of linear programming, geometry, and
approximation. Special attention is paid to applications of convex analysis to
Kolmogorov-type inequalities for derivatives of functions in one
variable. Chapter 3 collects some results on geometry and convex analysis in
infinite-dimensional spaces. A comprehensive introduction written “for
beginners” illustrates the fundamentals of convex analysis in
finite-dimensional spaces.

The book can be used for an advanced undergraduate or graduate-level course
on convex analysis and its applications. It is also suitable for independent
study of this important area of mathematics.